Solve No. Date x - (7/4 + 8/3) + 10/3 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$r - ( \frac { 7 } { 4 } + \frac { 8 } { 3 } ) + \frac { 10 } { 3 }$$

Evaluate

$r = -\frac{13}{12} = -1\frac{1}{12} = -1.0833333333333333$

Solution Steps

Least common multiple of $4$ and $3$ is $12$. Convert $\frac{7}{4}$ and $\frac{8}{3}$ to fractions with denominator $12$.

$$r-\left(\frac{21}{12}+\frac{32}{12}\right)+\frac{10}{3}$$

Since $\frac{21}{12}$ and $\frac{32}{12}$ have the same denominator, add them by adding their numerators.

$$r-\frac{21+32}{12}+\frac{10}{3}$$

Add $21$ and $32$ to get $53$.

$$r-\frac{53}{12}+\frac{10}{3}$$

Least common multiple of $12$ and $3$ is $12$. Convert $-\frac{53}{12}$ and $\frac{10}{3}$ to fractions with denominator $12$.

$$r-\frac{53}{12}+\frac{40}{12}$$

Since $-\frac{53}{12}$ and $\frac{40}{12}$ have the same denominator, add them by adding their numerators.

$$r+\frac{-53+40}{12}$$

Add $-53$ and $40$ to get $-13$.

$$r-\frac{13}{12}$$

Expand

$r = -\frac{13}{12} = -1\frac{1}{12} = -1.0833333333333333$

Solution Steps

Least common multiple of $4$ and $3$ is $12$. Convert $\frac{7}{4}$ and $\frac{8}{3}$ to fractions with denominator $12$.

$$r-\left(\frac{21}{12}+\frac{32}{12}\right)+\frac{10}{3}$$

Since $\frac{21}{12}$ and $\frac{32}{12}$ have the same denominator, add them by adding their numerators.

$$r-\frac{21+32}{12}+\frac{10}{3}$$

Add $21$ and $32$ to get $53$.

$$r-\frac{53}{12}+\frac{10}{3}$$

Least common multiple of $12$ and $3$ is $12$. Convert $-\frac{53}{12}$ and $\frac{10}{3}$ to fractions with denominator $12$.

$$r-\frac{53}{12}+\frac{40}{12}$$

Since $-\frac{53}{12}$ and $\frac{40}{12}$ have the same denominator, add them by adding their numerators.

$$r+\frac{-53+40}{12}$$

Add $-53$ and $40$ to get $-13$.

$$r-\frac{13}{12}$$